Problem: Before quantum mechanics was developed, Johannes Rydberg developed an equation that predicted the wavelengths (λlambda) in the atomic spectrum of hydrogen: 1/λ = R(1/m2 - 1/n2). In this equation R is a constant and m and n are integers. Use the quantum-mechanical model for the hydrogen atom to derive the Rydberg equation.

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  • For an H atom, the energy of an electron in level n is represented as:

  • An electron jumping from higher energy level f to lower energy level i, the energy released by atom will appear as:

  • Use the equation of En to find the ΔE.

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Before quantum mechanics was developed, Johannes Rydberg developed an equation that predicted the wavelengths (λ) in the atomic spectrum of hydrogen: 1/λ = R(1/m2 - 1/n2). In this equation R is a constant and m and n are integers. Use the quantum-mechanical model for the hydrogen atom to derive the Rydberg equation.